Mark invests $6,000 in an account.

Question

Mark invests $6,000 in an account. How long will it take for the investment to double if the annual interest rate is 5.5%, compounded monthly. Round the answer to two decimal places

Answer 1

Hey Keiana.

 

This is a simple plug 'n chug question from the simple interest formula.

 

A = P(1 + r/n)^nt

 

A = amount after time t

P = principal invested

r = interest rate

n = how many times a year its compounded

t = time

 

In your case:

 

A = 2*6000

P = 6000

r = 5.5% = 0.055

n = 12, since there are 12 months per year

t = ???

 

2*6000 = 6000(1 + 0.055/12)^12t

 

2 = (1 + 0.055/12)^12t

 

Take the natural log of both sides to bring the 12t down from the exponent.

 

ln(2) = ln(1 + 0.055/12)^12t

 

ln(2) = 12t*ln(1 + 0.055/12)

 

Solve for t.

 

ln(2)/ ln(1 + 0.055/12) = 12t

 

t = ln(2) / (12*ln(1 + 0.055/12))

 

t = 12.63 years

 

Hope this helps.